statistics

An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" (h) and "tails" (r) which we write hth, tri, etc. For each outcome, let R be the random variable counting the number of tails in each outcome. For example, if the outcome is http then R (hit) = 2. Suppose that the random variable .X' is defined in terms of R as follows: X = 6R-2R--2. The values of X are given in the table below. Outcome hht ttt hit the hhh thh tth hth Value of X 2 2 Calculate the values of the probability distribution function of X, Le. the function py. First, fill in the first row with the values of X. Then fill in the appropriate probabilities in the second row. Value X of X X ? Px (x)